The Reds were held to a 1-1 draw on the first day of the season by the Black Cats, a result that set the tone for seven further home stalemates at Anfield throughout the campaign so far.
However, Dalglish's men have won more games on their travels than at home and the Merseyside club’s manager hopes that their ability to pick up results on the road can be taken to the Stadium of Light.
The Scot told reporters: “A lot of performances at home have been of a high quality and haven't got the result they deserved but away from home we have got better results but maybe not been as attractive.
“We don't change too much wherever we play. We always want to win the game and we'll always put a team out we think is going to win.
“We want to win both places, home and away, and we have the capabilities to do so.”
Steve Bruce was the coach in charge at the North East club at the start of the season but was fired in November after a poor run of results led to the side languishing too near the relegation zone.
“It was a surprise to see Steve Bruce get the sack but obviously results were not impressive and it puts everyone under pressure,” Dalglish added.
“They have had a great turnaround [since Martin O'Neill was hired]. There are not that many players who have come in to change it so obviously they are playing with greater commitment and are playing much better now.
“The results give them confidence and belief which they didn't have beforehand.
“They've done very well since he went in there and made themselves very difficult to beat. It is going to be a difficult task for us."
After beating Cardiff City in the League Cup final, the Reds were hit with a comedown when Arsenal defeated them on their own turf last time out, but the former forward believes that Liverpool are going places.
He observed: “People who watch this club and who work here know the work which has been done and the turnaround which has taken place.
“We don't shout our mouth off about what we have done, where we have come from and where we want to go.
“We will continue to do our best in training and in matches.
“The players are enjoying what they are doing and coming into work and playing football - but it is much more enjoyable when you win.”